Question - Age Problem Solution with Algebra
Solution:
The image contains a math word problem that reads: "Richard and Tom have a combined age of 49. Richard is 3 years older than twice Tom's age. How old are Richard and Tom?"Let's use algebra to solve this problem. We'll let R represent Richard's age and T represent Tom's age.We have two pieces of information:1. Combined age: R + T = 492. Richard's age in relation to Tom's age: R = 3 + 2TNow we have two equations:(1) R + T = 49(2) R = 3 + 2TWe can substitute the value of R from equation (2) into equation (1):3 + 2T + T = 49Now combine like terms:3 + 3T = 49Subtract 3 from both sides to solve for T:3T = 49 - 33T = 46Now divide by 3 to get T:T = 46 / 3T = 15⅓However, ages are typically represented in whole numbers so the age should not be a fraction. Let's check our calculation to avoid any fraction since the question probably expects whole numbers as an answer.Dividing 46 by 3 again,T = 46 / 3T = 15 with a remainder of 1. This means that Tom's age is 15, not 15⅓.Now we can find Richard's age by substituting T back into equation (2):R = 3 + 2(15)R = 3 + 30R = 33So, Richard is 33 years old and Tom is 15 years old.
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